Simplify the following expression: $\dfrac{77k^5}{56k^2}$ You can assume $k \neq 0$.
Explanation: $ \dfrac{77k^5}{56k^2} = \dfrac{77}{56} \cdot \dfrac{k^5}{k^2} $ To simplify $\frac{77}{56}$ , find the greatest common factor (GCD) of $77$ and $56$ $77 = 7 \cdot 11$ $56 = 2 \cdot 2 \cdot 2 \cdot 7$ $ \mbox{GCD}(77, 56) = 7 $ $ \dfrac{77}{56} \cdot \dfrac{k^5}{k^2} = \dfrac{7 \cdot 11}{7 \cdot 8} \cdot \dfrac{k^5}{k^2} $ $\phantom{ \dfrac{77}{56} \cdot \dfrac{5}{2}} = \dfrac{11}{8} \cdot \dfrac{k^5}{k^2} $ $ \dfrac{k^5}{k^2} = \dfrac{k \cdot k \cdot k \cdot k \cdot k}{k \cdot k} = k^3 $ $ \dfrac{11}{8} \cdot k^3 = \dfrac{11k^3}{8} $